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Robust Shadow Estimation

Chen, Senrui and Yu, Wenjun and Zeng, Pei and Flammia, Steven T. (2021) Robust Shadow Estimation. PRX Quantum, 2 (3). Art. No. 030348. ISSN 2691-3399. doi:10.1103/prxquantum.2.030348.

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Efficiently estimating properties of large and strongly coupled quantum systems is a central focus in many-body physics and quantum information theory. While quantum computers promise speedups for many of these tasks, near-term devices are prone to noise that will generally reduce the accuracy of such estimates. Here, we propose a sample-efficient and noise-resilient protocol for learning properties of quantum states building on the shadow estimation scheme [Huang et al., Nature Physics 16, 1050–1057 (2020)]. By introducing an experimentally friendly calibration procedure, our protocol can efficiently characterize and mitigate noises in the shadow estimation scheme, given only minimal assumptions on the experimental conditions. When the strength of noises can be bounded, our protocol approximately retains the same order of sample efficiency as the standard shadow estimation scheme, while also possessing a provable noise resilience. We give rigorous bounds on the sample complexity of our protocol and demonstrate its performance with several numerical experiments, including estimations of quantum fidelity, correlation functions and energy expectations, etc., which highlight a wide spectrum of potential applications of our protocol on near-term devices.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Chen, Senrui0000-0002-5904-6906
Yu, Wenjun0000-0002-5273-719X
Zeng, Pei0000-0003-4016-0706
Flammia, Steven T.0000-0002-3975-0226
Additional Information:© 2021 The Author(s). Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. (Received 25 December 2020; accepted 23 August 2021; published 22 September 2021) We thank You Zhou for discussions on random unitary schemes, Yihong Zhang for suggestions about gate-dependent noise, Hsin-Yuan Huang and Jinguo Liu for helpful suggestions on the numerical simulations, and John Preskill for discussions on the noise assumptions. We also thank Xiongfeng Ma and Richard Kueng for many helpful comments. C.S., W.Y., and P.Z. are supported by the National Natural Science Foundation of China under Grants No. 11875173 and No. 11674193, the National Key Research and Development Program of China under Grants No. 2019QY0702 and No. 2017YFA0303903, and the Zhongguancun Haihua Institute for Frontier Information Technology. Note added.—After posting this paper to arXiv, two related but independent works subsequently appeared. The independent work by Koh and Grewal [69] also studies how to mitigate noise in the shadow estimation protocol. In their work, the noise channel is assumed to be completely precharacterized. The main results, Theorems 1.1 and 1.2, are similar to our Theorems 2 and 4 if our noise calibration procedure is assumed to be done perfectly. The other independent work by Berg et al. [70] also contains some similar ideas as presented in our work. We thank the authors for communicating their work with us.
Group:AWS Center for Quantum Computing
Funding AgencyGrant Number
National Natural Science Foundation of China11875173
National Natural Science Foundation of China11674193
National Key Research and Development Program of China2019QY0702
National Key Research and Development Program of China2017YFA0303903
Zhongguancun Haihua Institute for Frontier Information TechnologyUNSPECIFIED
Issue or Number:3
Record Number:CaltechAUTHORS:20210927-213255246
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:111052
Deposited By: George Porter
Deposited On:28 Sep 2021 14:14
Last Modified:28 Sep 2021 14:14

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